The real difference between the sound from a tube amp vs. a solid state one has to do with the way the amp responds to transients, ie. fast changes in the wave form or signal being amplified.
Valves tend to compress naturally when they are subject to overdriving. This also happens when they are being fed an already overdriven signal, although not as much.
Here's a solid state vs. tube amplifier being subjected to overdriving or "Clipping" - so called because it looks like someone took a pair of scissors and "clipped" off the tops of the waveforms.

When a valve is overdriven, its inherent natural compression tends to round out the sharp, clipped edges of the waveform, making this clipping sound more musical and less brittle and harsh.
Valves (The British way of saying "tubes") are natural compressors and have a relatively slow response to very sudden chnges in amplitude.
Now think about how this affects your ears. A sharply clipped waveform at the speaker translates into a very harsh movement of air generated by the speaker compared to when the corners of the clipped wave are made nice and smooth by a tube. All of this results in smoother, creamier tone, less brittle and harsh than solid state.
I'm a sufferer of tinnitus, though apparently not as severe as yours, and I don't play electric guitar through SS amps any more, as I find that the tube amps are far less jarring on my ears.
Valves tend to compress naturally when they are subject to overdriving. This also happens when they are being fed an already overdriven signal, although not as much.
Here's a solid state vs. tube amplifier being subjected to overdriving or "Clipping" - so called because it looks like someone took a pair of scissors and "clipped" off the tops of the waveforms.

When a valve is overdriven, its inherent natural compression tends to round out the sharp, clipped edges of the waveform, making this clipping sound more musical and less brittle and harsh.
Valves (The British way of saying "tubes") are natural compressors and have a relatively slow response to very sudden chnges in amplitude.
Now think about how this affects your ears. A sharply clipped waveform at the speaker translates into a very harsh movement of air generated by the speaker compared to when the corners of the clipped wave are made nice and smooth by a tube. All of this results in smoother, creamier tone, less brittle and harsh than solid state.
I'm a sufferer of tinnitus, though apparently not as severe as yours, and I don't play electric guitar through SS amps any more, as I find that the tube amps are far less jarring on my ears.